Abstract:
This paper considers a discrete-time model of a financial market with one risky asset and
one risk-free asset, where the asset price and wealth dynamics are determined by the
interaction of two groups of agents, fundamentalists and chartists. In each period each group
allocates its wealth between the risky asset and the safe asset according to myopic expected
utility maximization, but the two groups have heterogeneous beliefs about the price change
over the next period: the chartists are trend extrapolators, while the fundamentalists expect
that the price will return to the fundamental. We assume that investors' optimal demand for
the risky asset depends on wealth, as a result of CRRA utility. A market maker is assumed to
adjust the market price at the end of each trading period, based on excess demand and on
changes of the underlying reference price. The model results in a nonlinear discrete-time
dynamical system. With growing price and wealth processes, but it is reduced to a stationary
system in terms of asset returns and wealth shares of the two groups. It is shown that the longrun
market dynamics are highly dependent on the parameters which characterize agents'
behaviour as wen as on the initial condition. Moreover, for wide ranges of the parameters a
(locally) stable fundamental steady state coexists with a stable 'non-fundamental' steady state,
or with a stable closed orbit, where only chartists survive in the long run: such cases require the numerical and graphical investigation of the basins of attraction. Other dynamic scenarios
include periodic orbits and more complex attractors, where in general both types of agents
survive in the long run, with time-varying wealth fractions.
